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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
List three odd positive integers.
💡 Hint: Start counting from 1 and only include numbers not divisible by 2.
Question 2
Easy
Is the set of all odd positive integers finite or infinite?
💡 Hint: Consider how the odd positive integers continue indefinitely.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What defines a countable set?
- Must be finite
- Can be matched with positive integers
- Has no elements
💡 Hint: Think about how we define sizes of sets.
Question 2
True or False: The set of odd positive integers has more elements than the set of positive integers.
- True
- False
💡 Hint: Consider the mapping function we introduced.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if two sets have the same cardinality, and one of them is finite, then the other must be finite as well.
💡 Hint: Consider how bijections relate to the size of both sets.
Question 2
Demonstrate a bijection between the set of rational numbers and the set of positive integers, citing your methodology.
💡 Hint: Think about how you can systematically traverse all fractions.
Challenge and get performance evaluation